Re: Finding a formula for a sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg35130] Re: [mg35104] Finding a formula for a sum*From*: BobHanlon at aol.com*Date*: Tue, 25 Jun 2002 19:55:02 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 6/25/02 5:10:35 AM, Matthias.Bode at oppenheim.de writes: >when trying to find the number of diagonals in a convex polygon (all corners >on the perimeter of a circle) with n corners I came across that sum: > >+(n-3) ; up to here = diagonals in a triangle. > >+(n-3) ; up to here = diagonals in a quadrangle. > >+(n-4) ; up to here = diagonals in a pentagon. > >+(n-5) ; up to here = diagonals in a hexagon. > >+(n-6) ; up to here = diagonals in a heptagon. >and so on. > >I found the general formula (n*n -3*n)/2 with pencil and paper. > >How could I coax MATHEMATICA into helping me to find the generalization >in >this case - and of course for more difficult ones as well? It is just the number of ways of taking n things 2 at a time except that you must exclude the sides of the polygon. Binomial[n, 2]-n // Simplify (1/2)*(-3 + n)*n Bob Hanlon Chantilly, VA USA